Kevin is $2$ times as old as Gabriela. $12$ years ago, Kevin was $6$ times as old as Gabriela. How old is Gabriela now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Gabriela. Let Kevin's current age be $k$ and Gabriela's current age be $g$. The information in the first sentence can be expressed in the following equation: ${k = 2g}$ Twelve years ago, Kevin was $k - 12$ years old, and Gabriela was $g - 12$ years old. The information in the second sentence can be expressed in the following equation: ${k - 12 = 6(g - 12)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$, it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: ${k = 2g}$. Substituting this into our second equation, we get: ${2g} {-12 = 6(g - 12)}$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $2 g - 12 = 6 g - 72$. Solving for $g$, we get: $4 g = 60.$ $g = 15$.